4 ms·

Inverse Symbolic Calculator Plus

28 points by edwintorok 14y ago

royalsporks 14y ago
Nice app!
ivan_ah 14y ago
Basically, this app tries guess whether a floating point number specified by the user can be expressed as some multiple of pi, e or one of the other important math numbers. ex: You want to calculate 150[degrees] in radians. Simple you say, just convert using your calculator: 150 [degrees] = 2.35619449019 [rad]. However On an exam/homework you would lose marks for this answer since it is not given "the right way" (as a fraction of pi). Using this app you can find out that 2.35619449019 [rad] = (3*pi)/4 [rad] and get all points. Cool.
- wtallis 14y ago
  Definitely cool, even though it's overloaded at the moment. The HP-48 series calculators and their successors have commands to convert from floating point to the approximately equivalent rationals or fraction of pi, but not exponentials or radicals or anything else like that. The tolerance for the approximation is determined by how many digits of the floating point number the calculator is set to display, so if you know the denominator is supposed to be small, you can force the calculator to produce the right answer even if you have relatively few decimal digits to work with or if there's a lot of rounding error.
- rom16384 14y ago
  I prefer RIES [1], that does pretty much the same thing. You can download its source code (C, GPL licensed) [2] or try it on the webpage. Oblig. (relevant) xkcd [3]. [1] http://mrob.com/pub/ries/index.html http://mrob.com/pub/ries/index.html [2] http://mrob.com/pub/ries/src/ries.c.txt http://mrob.com/pub/ries/src/ries.c.txt [3] http://xkcd.com/1047/ http://xkcd.com/1047/
- pash 14y ago
  150/360 = 5/12, so 150 deg = 5pi/6 rad. Clearly we could use this calculator. :P
rtpg 14y ago
Is there a developed theory around this kind of work? This seems somehow related to various search strategies, but it'd be interesting to hear what sort of tools are exploited.
- bnegreve 14y ago
  Maybe machine learning, trying to build models from examples is very common problem in ML. For example, regression [1] seems close. [1] http://en.wikipedia.org/wiki/Regression_analysis http://en.wikipedia.org/wiki/Regression_analysis
- bentoner 14y ago
  http://en.wikipedia.org/wiki/Integer_relation_algorithm http://en.wikipedia.org/wiki/Integer_relation_algorithm
- jamessb 14y ago
  Yes - lattice reduction and integer relation detection. You can construct a basis that contains a load of constants (pi, pi/2, pi/3, sqrt(pi) etc), and combinations of constants (pi*e, e^pi etc). Then you can use an integer relation algorithm [1] like PSLQ [2,3] to find integer coefficients with which to express the desired number in terms of elements of the basis. [1] http://en.wikipedia.org/wiki/Integer_relation_algorithm http://en.wikipedia.org/wiki/Integer_relation_algorithm [2] http://arminstraub.com/files/pslq.pdf http://arminstraub.com/files/pslq.pdf [3] http://mathworld.wolfram.com/PSLQAlgorithm.html http://mathworld.wolfram.com/PSLQAlgorithm.html
Svip 14y ago
I tried entering 4, which it suggested 2/5 to be the best answer. I would have assumed it suggested 2+2, but apparently it cannot handle simple calculations. Since 2/5 is 0.4, I thought it was because just entering '4' meant '0.4', but entering '4.0' and it produced the same result.
- sp332 14y ago
  I you look at the results, it's just matching a sequence of digits. It's not looking at the decimal place at all.
tragomaskhalos 14y ago
Just gave it pi squared over 6 (1.6449340668482264), which is the sum to infinity of 1/n-squared, and it identified it as zeta(2) (http://en.wikipedia.org/wiki/Zeta_function http://en.wikipedia.org/wiki/Zeta_function). Impressive.
bencollier49 14y ago
There's been a recent blog by John D. Cook about doing the same thing with SymPy, which is fairly nifty: http://www.johndcook.com/blog/2013/04/30/recognizing-numbers/ http://www.johndcook.com/blog/2013/04/30/recognizing-numbers...
astralgeezer 14y ago
try 0
marshray 14y ago
Standard lookup results for 1 Best guess: 1/10

28 points by edwintorok 14y ago

Nice app!

Basically, this app tries guess whether a floating point number specified by the user can be expressed as some multiple of pi, e or one of the other important math numbers. ex: You want to calculate 150[degrees] in radians. Simple you say, just convert using your calculator: 150 [degrees] = 2.35619449019 [rad]. However On an exam/homework you would lose marks for this answer since it is not given "the right way" (as a fraction of pi). Using this app you can find out that 2.35619449019 [rad] = (3*pi)/4 [rad] and get all points. Cool.

wtallis 14y ago
Definitely cool, even though it's overloaded at the moment. The HP-48 series calculators and their successors have commands to convert from floating point to the approximately equivalent rationals or fraction of pi, but not exponentials or radicals or anything else like that. The tolerance for the approximation is determined by how many digits of the floating point number the calculator is set to display, so if you know the denominator is supposed to be small, you can force the calculator to produce the right answer even if you have relatively few decimal digits to work with or if there's a lot of rounding error.
rom16384 14y ago
I prefer RIES [1], that does pretty much the same thing. You can download its source code (C, GPL licensed) [2] or try it on the webpage. Oblig. (relevant) xkcd [3]. [1] http://mrob.com/pub/ries/index.html http://mrob.com/pub/ries/index.html [2] http://mrob.com/pub/ries/src/ries.c.txt http://mrob.com/pub/ries/src/ries.c.txt [3] http://xkcd.com/1047/ http://xkcd.com/1047/
pash 14y ago
150/360 = 5/12, so 150 deg = 5pi/6 rad. Clearly we could use this calculator. :P

rtpg 14y ago

Is there a developed theory around this kind of work? This seems somehow related to various search strategies, but it'd be interesting to hear what sort of tools are exploited.

bnegreve 14y ago
Maybe machine learning, trying to build models from examples is very common problem in ML. For example, regression [1] seems close. [1] http://en.wikipedia.org/wiki/Regression_analysis http://en.wikipedia.org/wiki/Regression_analysis
bentoner 14y ago
http://en.wikipedia.org/wiki/Integer_relation_algorithm http://en.wikipedia.org/wiki/Integer_relation_algorithm
jamessb 14y ago
Yes - lattice reduction and integer relation detection. You can construct a basis that contains a load of constants (pi, pi/2, pi/3, sqrt(pi) etc), and combinations of constants (pi*e, e^pi etc). Then you can use an integer relation algorithm [1] like PSLQ [2,3] to find integer coefficients with which to express the desired number in terms of elements of the basis. [1] http://en.wikipedia.org/wiki/Integer_relation_algorithm http://en.wikipedia.org/wiki/Integer_relation_algorithm [2] http://arminstraub.com/files/pslq.pdf http://arminstraub.com/files/pslq.pdf [3] http://mathworld.wolfram.com/PSLQAlgorithm.html http://mathworld.wolfram.com/PSLQAlgorithm.html

Svip 14y ago

I tried entering 4, which it suggested 2/5 to be the best answer. I would have assumed it suggested 2+2, but apparently it cannot handle simple calculations. Since 2/5 is 0.4, I thought it was because just entering '4' meant '0.4', but entering '4.0' and it produced the same result.

sp332 14y ago
I you look at the results, it's just matching a sequence of digits. It's not looking at the decimal place at all.

tragomaskhalos 14y ago

Just gave it pi squared over 6 (1.6449340668482264), which is the sum to infinity of 1/n-squared, and it identified it as zeta(2) (http://en.wikipedia.org/wiki/Zeta_function http://en.wikipedia.org/wiki/Zeta_function). Impressive.

bencollier49 14y ago

There's been a recent blog by John D. Cook about doing the same thing with SymPy, which is fairly nifty: http://www.johndcook.com/blog/2013/04/30/recognizing-numbers/ http://www.johndcook.com/blog/2013/04/30/recognizing-numbers...

astralgeezer 14y ago

try 0

marshray 14y ago

Standard lookup results for 1 Best guess: 1/10